Question

Let, the coefficient of variation of two datasets be $50$ and $75$ ,respectively and the corresponding variances be $25$ and $36$,respectively.Also let $x_1$ and $x_2$ denote the corresponding sample means. Then $x_1+x_2$ is ?

• A. $2$
• B. $10$
• C. $18$
• D. $16$
• E. $20$

Answer 1

Answer: (C)

$18$

Answer 2

Given data:

Let, the Co-efficient of variation of 1st data = $CV_1=50$

Let, the Co-efficient of variation of 2nd data = $CV_2=75$

and Variance $(σ_1^{2})=25$ . So, $σ_1=5$

    Variance $(σ_2^{2})=36$ . So, $ σ_1=6$

We know that,

$CV_1=\dfrac{σ_1}{x_1} × 100$

$⇒ x_1=\dfrac{5}{CV_1} × 100$

$⇒ x_1=\dfrac{5}{50} × 100$

$⇒ x_1=10$

Similarly solving for 2nd data we get

$⇒x_2=8$

Hence , $x_1+x_2=10+8=18$ (_Ans.)